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Anyway. The only complication at this point is the addition of a non-open-ended additional die, to be subtracted on a roll of 1 or added on a roll of 20. I quite like this kind of setup (first seen I think in Shadowrun).
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Nope.
Shadowrun used a dice pool system with d6s. If you rolled 6 on any one die, you rolled it again and added the six you just rolled. This allowed for a larger array of difficulties without using less-common dice. There weren't any separate dice used at all.
The system you're referring to doesn't sound familiar to me, though the Quality Die from
Chivalry & Sorcery and the Drama Die from Last Unicorn Games' Icon system both come to mind, as does Alternity, though it used different dice for bonuses and penalties rather than a fixed d20.